Chapter 27, Problem 27.25E

A proton (q = 1.60 × 10⁻¹⁹ C, m = 1.67 × 10⁻²⁷ kg) moves in a uniform magnetic field $\stackrel{\to }{\text{B}}$ = (0.500 T)i. At t = 0 the proton has velocity components ʋ_x = 1.50 × 10⁵ m/s, ʋ_y = 0, and ʋ_z = 2.00 × 10⁵ m/s (see Example 27.4). (a) What are the magnitude and direction of the magnetic force acting on the proton? In addition to the magnetic field there is a uniform electric field in the +x-direction, $\stackrel{\to }{\text{E}}$ = (+2.00 × 10⁴ V/m) $\hat{i}$. (b) Will the proton have a component of acceleration in the direction of the electric field? (c) Describe the path of the proton. Does the electric field affect the radius of the helix? Explain, (d) At t = T/2, where T is the period of the circular motion of the proton, what is the x-component of the displacement of the proton from its position at t = 0?